AP Calculus BC Quiz
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ANALYTICAL APPLICATIONS OF DIFFERENTIATION
Question 1
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Given
x
2
y
+
tan
(
x
y
)
=
0
x^2y+\tan(xy)=0
x
2
y
+
tan
(
x
y
)
=
0
, find
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
at a general point
(
x
,
y
)
(x,y)
(
x
,
y
)
.
A
−
2
x
y
−
y
sec
2
(
x
y
)
x
2
+
x
sec
2
(
x
y
)
\dfrac{-2xy-y\sec^2(xy)}{x^2+x\sec^2(xy)}
x
2
+
x
sec
2
(
x
y
)
−
2
x
y
−
y
sec
2
(
x
y
)
B
2
x
y
+
y
sec
2
(
x
y
)
x
2
+
x
sec
2
(
x
y
)
\dfrac{2xy+y\sec^2(xy)}{x^2+x\sec^2(xy)}
x
2
+
x
sec
2
(
x
y
)
2
x
y
+
y
sec
2
(
x
y
)
C
−
2
x
y
−
y
sec
2
(
x
y
)
x
2
−
x
sec
2
(
x
y
)
\dfrac{-2xy-y\sec^2(xy)}{x^2-x\sec^2(xy)}
x
2
−
x
sec
2
(
x
y
)
−
2
x
y
−
y
sec
2
(
x
y
)
D
−
2
x
y
x
2
+
x
sec
2
(
x
y
)
\dfrac{-2xy}{x^2+x\sec^2(xy)}
x
2
+
x
sec
2
(
x
y
)
−
2
x
y
E
−
2
x
y
−
y
sec
2
(
x
y
)
d
y
d
x
x
2
+
x
sec
2
(
x
y
)
\dfrac{-2xy-y\sec^2(xy)\,\dfrac{dy}{dx}}{x^2+x\sec^2(xy)}
x
2
+
x
sec
2
(
x
y
)
−
2
x
y
−
y
sec
2
(
x
y
)
d
x
d
y
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